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The discrete time wavelet transform: its discrete time Fourier transform and filter bank implementation

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2 Author(s)
M. T. Hanna ; Dept. of Eng. Math. & Phys., Cairo Univ., Fayoum, Egypt ; S. A. Mansoori

Viewing the discrete time wavelet transform DTWT[m,n] of a sampled signal s(nT) as a sequence in n, a closed-form expression is derived for its Discrete Time Fourier Transform (DTFT) D(m)(e) in terms of the DTFTs of the sampled mother wavelet ψ(nT) and sampled signal s(nT). Next, an expression is derived for the output Y(m)(e) of a filter bank defined by the digital filters a[n] and b[n] and excited by s(nT). The filter a[n] emerged as an ideal low-pass filter, and the filter b[n] turned out to be a time-reversed and complex conjugated version of the sampled mother wavelet ψ(nT)

Published in:

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing  (Volume:48 ,  Issue: 2 )